9x(5x-4)=12(2x+5)

Solution for 9x(5x-4)=12(2x+5) equation:

9x(5x-4)=12(2x+5)

We move all terms to the left:

9x(5x-4)-(12(2x+5))=0

We multiply parentheses

45x^2-36x-(12(2x+5))=0


We calculate terms in parentheses: -(12(2x+5)), so:

12(2x+5)

We multiply parentheses

24x+60

Back to the equation:

-(24x+60)


We get rid of parentheses

45x^2-36x-24x-60=0

We add all the numbers together, and all the variables

45x^2-60x-60=0

a = 45; b = -60; c = -60;
Δ = b2-4ac
Δ = -602-4·45·(-60)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-120}{2*45}=\frac{-60}{90}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+120}{2*45}=\frac{180}{90}
=2
$